4 citations · 4 across the 9 of their papers we have counts for
7 papers · 1 filter
Quadratic and -th variation of random signed Takagi--Landsberg bridges
Purba Das, Alexander Schied
We study random signed Takagi--Landsberg bridges with independent Rademacher Faber--Schauder coefficients. At index , we prove that every fixed deterministic refining sequen…
Banach spaces of continuous paths with finite -th variation
Purba Das, Donghan Kim, Fang Rui Lim
We study pathwise -th variation of continuous paths on a compact interval along a fixed partition sequence. Although the class of continuous paths with finite -th variation i…
On isomorphism of the space of continuous functions with finite -th variation along a partition sequence
Purba Das, Donghan Kim
We study the concept of (generalized) -th variation of a real-valued continuous function along a general class of refining sequence of partitions. We show that the finiteness of…
Level crossings of fractional Brownian motion
Purba Das, Rafał Łochowski, Toyomu Matsuda +1
Since the classical work of Lévy, it is known that the local time of Brownian motion can be characterized through the limit of level crossings. While subsequent extensions of this…
Hölder regularity and roughness: construction and examples
Erhan Bayraktar, Purba Das, Donghan Kim
We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorph…
Quadratic variation along refining partitions: Constructions and Examples
Rama Cont, Purba Das
We present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions, extending previous constructions to the non-uniform…
Quadratic variation and quadratic roughness
Rama Cont, Purba Das
We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We define t…